Volume of Composite Rectangular Prisms

Welcome to math with Mr. In this video, I'm going to be covering how to calculate the volume of composite rectangular prism. And if you take look at your screen, you'll see two composite rectangular prisms, and we're going to find the volume of both of those in order to help you get this down. Now, you might remember or maybe you've forgotten this is quick refresher, but the formula for volume that we are going to use is length times width times height. And remember volume is the amount of space three-dimensional object takes up. And as you can see, these aren't just plain old rectangular prisms, they're little more complex, so it takes couple extra steps, but the foundation of finding the volume is still going to be that formula. So, let's jump right into number one here. And when we have composite rectangular prisms, the first thing we want to do is cut that figure into two separate rectangular prisms. So, I'm going to draw line here that's going to separate this into left and right rectangular prism. I'm going to call the left-hand one and the right-hand one Again, cut the complex or composite figure into two rectangular prisms. Now, what we're going to do is find the volume of the volume of and add those together, and that's going to give us the volume of the composite rectangular prism. So, let's do first. So, I'm going to put our and And then let's write out our formula for each. And once we get to this part, it's about picking out the correct lengths, widths, and heights for and So, again, let's do first. So, we need the length, and consider the length how far back that rectangular prism goes. So, we're going to want to see how far back. And that's going to be 4 in. Times how wide is So, goes from there to there. So, we're not going to use that 10 in. That's common mistake using incorrect measurements. That 10 in goes all the way across. We just want right here. So, we're going to have to look around this rectangular prism in order to find the correct number. And if you look up top, we have 3 in that matches with the width. So, we're going to plug in that three. And next is the height. And we could look here at this 4 in for that. So, we need to do 4 * 3 * 4 in order to calculate the volume of part 4 * 3 is 12 * 4 is 48, and these are cubic inches. Now, we're halfway done with the problem because that is the volume of just Now, we need to do So, the length, how far back? Well, 4 in. Times the width, again, don't use that 10. That 10 goes all the way across. That includes and We just want the width here, which is going to be 7 in. And then the height, well, isn't this full 4 in that we used for It's little bit shorter, so let's look back here and this 2 in is our height for So, 4 * 7 is 28 times 2 is 56, and that's cubic inches. So, now to wrap up the problem, I'm going to go to the top left of the screen where have some room here. We need to do which is 56, plus 48, to get the total volume. And we get to 104 cubic inches. So, our answer for number one is 104 cubic inches. All right, let's take look at number two. actually, before we move to number two, do want to mention for something for number one, and this actually applies to all of the composite rectangular prisms. There is more than one way to cut them or split them into two rectangular prisms. So, for number one, have left and right. could have, if you take look where my letter is, could have cut it here, so had top and bottom rectangular prism. would have gotten to the same answer of 104. So, for number two, I'm actually going to cut it so there is top and bottom rectangular prism. So, I'm going to name the top and the bottom Giving them name helps helps stay organized throughout the problem. So, we're going to set it up the same way as we did number one. So, let's put our formulas, and then it's just going to be matter of picking out the correct dimensions. So, for we need to take look at length. How far back does go? Well, the whole shape actually goes the whole rectangular prism goes back 4 ft, so we're going to use this four for the length. how wide? Well, we could look up top here and see 2 ft. And then the height, we don't want to use this eight over here. We don't want to use that eight because that's the whole height of and We just want which is going to be this 5 ft here. So, we get to 4 * 2 is 8 * 5 is 40 cubic feet. Now, for the length, well, that whole rectangular prism or composite rectangular prism, all of it goes back 4 ft, which again, we use this four here. And then we need to multiply by the width. Now, does go all the way across, so we can use the seven. Don't use this five here. That five won't be used. It doesn't go all the way across. So, again, we need this seven. And then times the height, don't use the eight because again, the eight is all the way up. It includes and So, we want right here, which is this 3 ft. You do not have to use all of the numbers when you get to these types of problems. So, 4 * 7 is 28, and then 28 * 3 is 84. Cubic feet. So, we get to 40 plus 84, which is going to give us 124 cubic feet. So, I'm going to write it inside of our composite rectangular prism here because I'm running out of room. So, 124 cubic feet. So, there you have it. There's how to calculate the volume of composite rectangular prisms. Break your figure down into two rectangular prisms, and then add those volumes together to get the volume of the entire figure. Hopefully that helped. Thanks so much for watching. Until next time, peace.